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Israel is to build hundreds of new homes in a settlement in the occupied West Bank where a Palestinian stabbed three Israelis, one fatally, Defence Minister Avigdor Lieberman said on Friday.

"The best answer to terrorism is the expansion of settlements," Mr Lieberman wrote on Twitter, announcing 400 new housing units in the Adam settlement north of Jerusalem a day after the deadly stabbing.

The teenage attacker snuck into the settlement on Thursday evening, the Israeli army said, stabbing three people before being shot dead.

Israel's military on Friday searched the West Bank village of the teenager.

The military said it detained four Palestinians for questioning and set up security inspections at entrances to Kauber, the assailant's village, north of Jerusalem. The attacker, identified as Mohammed Tareq Dar Yousef, 17, by family members was shot and killed at the scene Thursday night.

The army named the man who died as Yotam Ovadia, 31, with Israeli media saying he had two young children.

Blood stains were still visible outside the home of the Israeli victim on Friday as relatives and friends gathered nearby.

The attacker was later identified by official Palestinian media as Mohammed Dar Youssef, 17, from the village of Kobar.

The attack came amid relative quiet in the West Bank, though there has been recurrent violence between the Israeli army and Palestinian groups in the besieged Gaza Strip in which at least 154 Palestinians have been killed.

In a statement Hamas, which runs Gaza, praised the "courageous operation" without claiming responsibility for it.

"The West Bank is ready and able to avenge the blood of the martyrs."

All settlement construction in the occupied West Bank is considered illegal by the international community.